“…(3) Where: P 1 , P 2 are pressures at points 1and 2 respectively, Pa, z 1 , z 2 are elevation from same reference line at points 1, and 2 respectively, m, v 1 , v 2 are velocity at points 1 and 2 respectively, m/s, h p is the pump head, m, h T is the Turbine Head, m, h L major is the losses due to friction, m, h L minor is the losses due to fittings, m, α is the coefficient of loss due to sudden expansion or contraction, g is the gravitational acceleration, 9.81 m/sec Engineering applications for piping systems could be as simple as a single pipe conveying a fluid from one reservoir to another or as complicated as a system of interconnected pipes forming a large distribution network [2]. In modeling such large networks, optimal demand allocation is necessary in order to prevent the network topology from getting too complicated and the network modeling from being too cumbersome [3,2] and other applications like psychometric charts [4].…”